Bobby McMann and Nicolas Roy each had a goal and an assist, and Nicholas Robertson had two assists for the Maple Leafs (18-15-6), who are 3-0-1 in their past four games.
Toronto played without captain Auston Matthews, who is day to day with a lower-body injury he sustained while blocking a shot with his foot in a 3-2 overtime loss to the Detroit Red Wings on Sunday. Forward William Nylander (lower body) and defenseman Chris Tanev (lower body) also did not play.
“Everyone was doing their job, goaltender was really good. Just all around pretty solid hockey by everybody,” Toronto coach Craig Berube said. “That’s the one thing I take from it, everybody bought in.”
Jacob Markstrom made 26 saves for the Devils (20-17-2), who are 0-3-1 in their past four games.
“We need some guys that are going to show a little bit more,” New Jersey coach Sheldon Keefe said. “If you're not going to score, give us a little bit more competitively and physically and show that you're working to find your way."
Woll kept it scoreless at 12:23 of the first period when he stopped a point-blank shot in the slot from Ondrej Palat, who one-timed a pass from Jack Hughes, who was behind the net.
“Just feeling the puck early is nice,” Woll said. “Any time you get shots early and make big saves early, I think that definitely helps you get engaged and get in the game."
The Maple Leafs then went ahead 1-0 at 14:21 of the first while on a power play. Robertson gloved down a clearing attempt at the blue line and passed across to McMann, who scored blocker side from the high slot.